Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

Spherical images contain full 360 ◦ visual information of recorded locations. By sharing such an image, it is possible to reproduce immersive sense of a remote location. This paper proposes a remote home appliances control interface that uses spherical images on a mobile console. It allows users to control remote devices intuitively.

OBJECTIVE The natural distribution and predictive accuracy of Bishop scores was evaluated to predict cesarean delivery (CD) in nulliparas between 37 and 42 weeks gestation. STUDY DESIGN Subjects underwent serial digital cervical examinations. The Bishop score was evaluated as a binary and continuous factor to predict CD at each gestational week beginning at 37 weeks. Bishop scores were catego...

1. Write the formula for the Liouville measure Λ on the unit tangent bundle T 1 H n. Prove that Λ is invariant under the actions by Isom(H n) and the geodesic flow g t on T 1 H n. 2. Let δ be a geodesic in the hyperbolic space H n and let π : H n → δ denote the nearest point projection map. Suppose that for some x, y ∈ H n and some r > 0 we have d(x, δ), d(y, δ) ≥ r. Prove that d(π(x), π(y)) ≤ ...

We propose in this chapter to consider the emerging framework of networks of omnidirectional cameras. We first describe how omnidirectional images captured by different types of mirrors or lenses can be uniquely mapped to spherical images. Spherical imaging can then be used for calibration, scene analysis or distributed processing in omni-directional camera networks. The chapter then presents c...

The ability to rely on similarity metrics invariant to image transformations is an important issue for image classification tasks such as face or character recognition. We analyze an invariant metric that has performed well for the latter the tangent distance and study its limitations when applied to regular images, showing that the most significant among these (convergence to local minima) can...

We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...

In this paper, we have proposed a method for 2D image retrieval based on object shapes. The method relies on transforming the 2D images into 3D space based on distance transform. Spherical harmonics are obtained for the 3D data and used as descriptors for the underlying 2D images. The proposed method is compared against two existing methods which use spherical harmonics for shape based retrieva...